The rapid emergence and expansion of novel SARS-CoV-2 variants is an unpleasant surprise that threatens our ability to achieve herd immunity for COVID-19 . These fitter SARS- CoV-2 variants often harbor multiple point mutations, conferring one or more traits that provide an evolutionary advantage, such as increased transmissibility, immune evasion and longer infection duration . In a number of cases, variant emergence has been linked to long-term infections in individuals who were either immunocompromised or treated with convalescent plasma . In this paper, we explore the mechanism by which fitter variants of SARS-CoV-2 arise during long-term infections using a mathematical model of viral evolution and identify means by which this evolution can be slowed . While viral load and infection duration play a strong role in favoring the emergence of such variants, the overall probability of emergence and subsequent transmission from any given infection is low, suggesting that viral variant emergence and establishment is a product of random chance . To the extent that luck plays a role in favoring the emergence of novel viral variants with an evolutionary advantage, targeting these low-probability random events might allow us to tip the balance of fortune away from these advantageous variants and prevent them from being established in the population.